Optimality conditions constrained optimisation

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Presentation transcript:

Optimality conditions constrained optimisation for constrained optimisation

Recall: Optimisation conditions for unconstrained problem with one variable function

Recall: Optimisation conditions for unconstrained problem with several variables function

Lagrangean multipliers

Lagrangean multipliers

Optimisation conditions for constrained problem

First order Karush-Kuhn-Tucker (KKT) optimality conditions

Sufficiency of the K-K-T conditions

Sufficiency of the K-K-T conditions

Sufficiency of the K-K-T conditions

Necessity of the K-K-T conditions

Kuhn-Tucker constraints qualification

K-K-T condition for linear programming

K-K-T condition for linear programming

K-K-T condition for linear programming

K-K-T condition for linear programming